module defpi
    implicit none
    real(8),parameter::pi=3.14159265358979323846D0
end module defpi

program f08_GAMMA
    use defpi
    implicit none
    integer::i,n
    real(8)::a,b,x,z

    n=200
    a=-5.0D0
    b= 5.0D0
    do i=0,n
        x=a+(b-a)/dble(n)*dble(i)
        if(0.0D0<x)then
            z=sqrt(2.0D0*pi/x)*(x/exp(1.0D0)*sqrt(x*sinh(1.0D0/x)+1.0D0/810.0D0/x**6.0D0))**x
        else
            z=-999.0D0
        end if
        write(6,'(3f12.5)') x,gamma(x),z
    end do

end program f08_GAMMA